The design optimization of optical systems is conventionally accomplished by iteratively adjusting a number of parameters until the best performance is obtained. These parameters include such things as curvature of the lenses, their refractive indexes, relative spacing between the lenses, etc. When a holographic (diffractive) optical element (HOE) is included in these optical systems, the parameters also consist of the descriptions of the two recording beams, the object and reference beam, used to record the HOE, which descriptions may include, for example, the wavelength of the recording beams and the parameters of the optical systems used to produce the recording beams.
The performance of an optical system is often measured in accordance with relative value of a variable known as a merit function. In the conventional system design approach a certain set of parameters is changed and then the merit function is monitored. If the merit function decreases (0 being the best value) the set of parameters will continue to be changed along the previous direction until adverse results began to occur; then a new direction of parameter changes is investigated. This is effectively a trial and error approach which takes a considerable amount of time. Another problem is that there is no guarantee that any optimization procedure will actually find the optimum values of all the parameters. Still another problem for optical systems utilizing HOE's is that any finite set of parameters cannot describe all possible system variables and therefore an optimum system may not be describable by the parameters employed.
The following papers discuss representative examples of conventional optical system design techniques: D. S. Grey, "Aberration Theories for Semiautomatic Lens Design by Electronic Computers (Parts I and II)", Journal of the Optical Society of America, Volume 53, No. 6, 672 (1963); and R.C. Fairchild and J.R. Fienup, "Computer-Originated Aspheric Holographic Optical Elements", Optical Engineering, Volume 21, No. 1 (1982). An excellent discussion, from a historical standpoint, of various design techniques is found in Feder, "Automatic Optical Design", Applied Optics, Volume 2, No. 12 (1963).
Even with the use of today's high speed computers, the task of quickly and accurately designing an optimum optical system using the various known iterative processes is, at best, a time consuming and arduous task.
The present invention is directed to a technique for quickly and accurately determining the construction of an optical system having the best merit function for any given set of parameters.